Implementation of Bayesian Inference in Distributed Neural Networks

Numerous neuroscience experiments have suggested that the cognitive process of human brain is realized as probability reasoning and further modeled as Bayesian inference. It is still unclear how Bayesian inference could be implemented by neural underpinnings in the brain. Here we present a novel Bayesian inference algorithm based on importance sampling. By distributed sampling through a deep tree structure with simple and stackable basic motifs for any given neural circuit, one can perform local inference while guaranteeing the accuracy of global inference. We show that these task-independent motifs can be used in parallel for fast inference without iteration and scale-limitation. Furthermore, experimental simulations with a small-scale neural network demonstrate that our distributed sampling-based algorithm, consisting with our theoretical analysis, can approximate Bayesian inference. Taken all together, we provide a proofof-principle to use distributed neural networks to implement Bayesian inference, which gives a road-map for large-scale Bayesian network implementation based on spiking neural networks with computer hardwares, including neuromorphic chips.